Michael, I can’t see much of your chain bar, only the bit up near the sprocket, which tends to wear the least, but the bit I can see appears not to have suffered too badly as a result of running an obviously dull, poorly lubricated (have you checked that the chain oil is reaching the bar and chain unimpeded?), and possibly loose chain.
Are there any areas further towards the bar nose where the paint has come off through overheating and the metal has discoloured? Is there any peening over of the bar groove, even slightly?
I’m sure you realise this but, aside from other undesirable outcomes, running a dull chain can also shorten engine life considerably, because when cutting with a dull chain there is little to no load on the engine to keep the revs within check. A properly sharpened chain will feed itself into the wood almost effortlessly and produce healthy engine sounds: a dull chain will produce dust (not chips) and make the engine scream ineffectually, while little progress is made in actually cutting any wood.
Assuming your bar is worth saving (and check also the condition of the sprocket), I would almost certainly not want to use that chain again even if sharpened well: the drive links will probably be worn, making for greater slop in the bar groove, which, even if the chain is correctly sharpened, well lubed and optimally tensioned, will accelerate wear on your bar and sprocket.
You need a 4mm round file for that chain (i.e. the new 3/8″ Picco chain you’ve yet to buy). If you can stretch to it, buy one of the Stihl part numbers 5605 750 4303 or 5605 007 1027. The latter can be had for around £11. I have both types in several sizes and they work very well indeed. The 2-in-1 type particularly makes the whole job of sharpening a chain to “cat’s claw” levels of sharpness astoundingly easy.
On the subject of stretching, when you’ve fitted your new chain, you must watch the tension very carefully in the first hour or so of use – a new chain stretches considerably, and can become very loose in a short time, which of course is undesirable for all sorts of reasons. Remember to allow the bar and chain to cool down after use before checking and adjusting chain tension.
Personally, I always slacken off my chains after use so that contraction on cooling doesn’t stress the bar or sprocket while the saw is in storage. An additional benefit of this is that you get into the habit of checking and adjusting chain tension before the next use, which avoids potential problems arising from firing up your saw and getting stuck into a job whilst complacently assuming that the chain is properly tensioned “because it was when I last used it”. Before starting, always assume it isn’t.